2. (Import 'Ihriffs) Consider a two-period open economy in which house- holds have preferences given by + InC'2 where CI and C2 denote, consumption of food in periods I and 2, mea- sured in tons. The country does not produce food. Households are endowed with QI and barrels of oil in periods I and 2. In both periods, a barrel of oil sells for one ton of food in international mar- ket.s. The economy starts period I with no assets, 130 = 0. The world interest rate is r' and there, is free capital mobility. 'The government, imposes tariffs on food imports in periods I and 2, denoted rl and r,2, and rebates the revenue generated by the tariffs to the public, using lump-sum transfers, denoted and (b) (d) (e) (f) (g) (h) What. are the terms of trade, in periods I and 2? Derive the household's intern:mporal budget constraint. Write down the, optimization problem of the household. Derive the, first,-order conditions of the household's optimization problem. Write down the budget constraints of the government in periods 1 and 2. Combine the, household's intertmmporal budget constraint with the government budget constraints to find the economy's intertempo- ral resource constraint in equilibrium. Do the policy variables 72, 1.1 , or appear in this constraint? Why? Let Y QI (22/(1 r') denote the present discounted value of the, endowment path. Express the equilibrium values of consump- tion in periods I and 2 in terms of Y , r', T, , and T2. Write the equilibrium trade balance in period 1 in terms of Y , r', QI, r, , and 72. Compare, the, trade balance under free trade, i.e., = = 0, to the following cases: (a) Tl = 72 > (b) T, > 0 and = O; and (c) = and 7-2 > O.